Asymptotics of H-identities for associative algebras with an H-invariant radical

作者：Gordienko A S^*

来源：Journal of Algebra, 2013, 393: 92-101.

DOI：10.1016/j.jalgebra.2013.05.032

• Associative algebra
• Polynomial identity
• Derivation
• Group action
• Hopf algebra
• H-module algebra
• Codimension
• Cocharacter
• Young diagram

We prove the existence of the Hopf PI-exponent for finite dimensional associative algebras A with a generalized Hopf action of an associative algebra H with 1 over an algebraically closed field of characteristic 0 assuming only the invariance of the Jacobson radical J(A) under the H-action and the existence of the decomposition of A/J(A) into the sum of H-simple algebras. As a consequence, we show that the analog of Amitsur%26apos;s conjecture holds for G-codimensions of finite dimensional associative algebras over a field of characteristic 0 with an action of an arbitrary group G by automorphisms and anti-automorphisms and for differential codimensions of finite dimensional associative algebras with an action of an arbitrary Lie algebra by derivations.

• 出版日期2013-11-1